Complexity_C_Integer 2019-03-21 04.38 pair #429989236

details
property	value
status	complete
benchmark	AliasDarteFeautrierGonnord-SAS2010-complex_true-termination.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	Adapted_from_Stroeder_15
run statistics
property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	1.79922 seconds
cpu usage	2.64673
user time	2.41936
system time	0.227362
max virtual memory	1.8454892E7
max residence set size	183544.0
stage attributes
key	value
starexec-result	WORST_CASE(?, O(n^1))
output
2.56/1.75	WORST_CASE(?, O(n^1))
2.59/1.76	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.59/1.76	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.59/1.76	
2.59/1.76	
2.59/1.76	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.59/1.76	
2.59/1.76	(0) CpxIntTrs
2.59/1.76	(1) Koat Proof [FINISHED, 478 ms]
2.59/1.76	(2) BOUNDS(1, n^1)
2.59/1.76	
2.59/1.76	
2.59/1.76	----------------------------------------
2.59/1.76	
2.59/1.76	(0)
2.59/1.76	Obligation:
2.59/1.76	Complexity Int TRS consisting of the following rules:
2.59/1.76	eval_foo_start(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b)) :|: TRUE
2.59/1.76	eval_foo_bb0_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_foo_bb1_in(v_a, v_b, v_.1, v_.12, v_a, v_b)) :|: TRUE
2.59/1.76	eval_foo_bb1_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.0, v_.01, v_a, v_b)) :|: v_.0 < 30
2.59/1.76	eval_foo_bb1_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b)) :|: v_.0 >= 30
2.59/1.76	eval_foo_bb2_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b)) :|: v_.12 < v_.1
2.59/1.76	eval_foo_bb2_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b)) :|: v_.12 >= v_.1
2.59/1.76	eval_foo_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.1 + 10, v_.12 + 7, v_a, v_b)) :|: v_.12 > 5 && v_.12 + 7 >= 10 && v_.12 + 7 <= 12
2.59/1.76	eval_foo_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.1 + 1, v_.12 + 7, v_a, v_b)) :|: v_.12 > 5 && v_.12 + 7 < 10
2.59/1.76	eval_foo_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.1 + 1, v_.12 + 7, v_a, v_b)) :|: v_.12 > 5 && v_.12 + 7 > 12
2.59/1.76	eval_foo_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.1 + 10, v_.12 + 2, v_a, v_b)) :|: v_.12 <= 5 && v_.12 + 2 >= 10 && v_.12 + 2 <= 12
2.59/1.76	eval_foo_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.1 + 1, v_.12 + 2, v_a, v_b)) :|: v_.12 <= 5 && v_.12 + 2 < 10
2.59/1.76	eval_foo_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.1 + 1, v_.12 + 2, v_a, v_b)) :|: v_.12 <= 5 && v_.12 + 2 > 12
2.59/1.76	eval_foo_bb4_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_foo_bb1_in(v_.1 + 2, v_.12 - 10, v_.1, v_.12, v_a, v_b)) :|: TRUE
2.59/1.76	eval_foo_bb5_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_foo_stop(v_.0, v_.01, v_.1, v_.12, v_a, v_b)) :|: TRUE
2.59/1.76	
2.59/1.76	The start-symbols are:[eval_foo_start_6]
2.59/1.76	
2.59/1.76	
2.59/1.76	----------------------------------------
2.59/1.76	
2.59/1.76	(1) Koat Proof (FINISHED)
2.59/1.76	YES(?, 35*ar_1 + 6*ar_3 + 1200)
2.59/1.76	
2.59/1.76	
2.59/1.76	
2.59/1.76	Initial complexity problem:
2.59/1.76	
2.59/1.76	1:	T:
2.59/1.76	
2.59/1.76			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.59/1.76	
2.59/1.76			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.59/1.76	
2.59/1.76			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ 29 >= ar_0 ]
2.59/1.76	
2.59/1.76			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 30 ]
2.59/1.76	
2.59/1.76			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_5 + 1 ]
2.59/1.76	
2.59/1.76			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= ar_4 ]
2.59/1.76	
2.59/1.76			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 10, ar_5 + 7)) [ ar_5 >= 6 /\ ar_5 >= 3 /\ 5 >= ar_5 ]
2.59/1.76	
2.59/1.76			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5 + 7)) [ ar_5 >= 6 /\ 2 >= ar_5 ]
2.59/1.76	
2.59/1.76			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5 + 7)) [ ar_5 >= 6 ]
2.59/1.76	
2.59/1.76			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 10, ar_5 + 2)) [ 5 >= ar_5 /\ ar_5 >= 8 /\ 10 >= ar_5 ]
2.59/1.76	
2.59/1.76			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5 + 2)) [ 5 >= ar_5 /\ 7 >= ar_5 ]
2.59/1.76	
2.59/1.76			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5 + 2)) [ 5 >= ar_5 /\ ar_5 >= 11 ]
2.59/1.76	
2.59/1.76			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4 + 2, ar_1, ar_5 - 10, ar_3, ar_4, ar_5))
2.59/1.76	
2.59/1.76			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.59/1.76	
2.59/1.76			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.59/1.76	
2.59/1.76		start location:	koat_start
2.59/1.76	
2.59/1.76		leaf cost:	0
2.59/1.76	
2.59/1.76	
2.59/1.76	
2.59/1.76	Testing for reachability in the complexity graph removes the following transitions from problem 1:
2.59/1.76	
2.59/1.76		evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 10, ar_5 + 7)) [ ar_5 >= 6 /\ ar_5 >= 3 /\ 5 >= ar_5 ]
2.59/1.76	
2.59/1.76		evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5 + 7)) [ ar_5 >= 6 /\ 2 >= ar_5 ]
2.59/1.76	
2.59/1.76		evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 10, ar_5 + 2)) [ 5 >= ar_5 /\ ar_5 >= 8 /\ 10 >= ar_5 ]
2.59/1.76	
2.59/1.76		evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5 + 2)) [ 5 >= ar_5 /\ ar_5 >= 11 ]
2.59/1.76	
2.59/1.76	We thus obtain the following problem:
2.59/1.76	
2.59/1.76	2:	T:
2.59/1.76	
2.59/1.76			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_4 + 2, ar_1, ar_5 - 10, ar_3, ar_4, ar_5))
2.59/1.76	
2.59/1.76			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5 + 2)) [ 5 >= ar_5 /\ 7 >= ar_5 ]
2.59/1.76
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actions all output return to Complexity_C_Integer 2019-03-21 04.38